Question

in the figure below, m∠4 = 67°. find m∠1, m∠2, and m∠3.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles. So $m\angle1=m\angle4 = 67^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, then $m\angle2=180 - m\angle1$. Substituting $m\angle1 = 67^{\circ}$, we get $m\angle2=180 - 67=113^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3=m\angle2 = 113^{\circ}$.

Answer:

$m\angle1 = 67^{\circ}$
$m\angle2 = 113^{\circ}$
$m\angle3 = 113^{\circ}$